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A369040 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A342014(i) = A342014(j), for all i, j >= 1.

%I A369040 #9 Jan 18 2024 18:13:22
%S A369040 1,2,2,3,2,4,2,5,6,7,2,8,2,9,10,11,2,12,2,13,14,15,2,16,14,17,18,19,2,
%T A369040 20,2,21,22,23,24,25,2,26,27,28,2,29,2,30,31,32,2,33,22,34,35,36,2,37,
%U A369040 27,38,39,40,2,41,2,42,43,44,45,46,2,47,48,49,2,50,2,31,51,52,45,53,2,54,55,56,2,57,39,34,58,59,2,60,35
%N A369040 Lexicographically earliest infinite sequence such that a(i) = a(j) => A003415(i) = A003415(j) and A342014(i) = A342014(j), for all i, j >= 1.
%C A369040 Restricted growth sequence transform of the ordered pair [A003415(n), A342014(n)].
%C A369040 For all i, j >= 1:
%C A369040   A369050(i) = A369050(j) => a(i) = a(j), [Conjectured]
%C A369040   a(i) = a(j) => A341625(i) = A341625(j).
%H A369040 Antti Karttunen, <a href="/A369040/b369040.txt">Table of n, a(n) for n = 1..100000</a>
%o A369040 (PARI)
%o A369040 up_to = 100000;
%o A369040 rgs_transform(invec) = { my(om = Map(), outvec = vector(length(invec)), u=1); for(i=1, length(invec), if(mapisdefined(om,invec[i]), my(pp = mapget(om, invec[i])); outvec[i] = outvec[pp] , mapput(om,invec[i],i); outvec[i] = u; u++ )); outvec; };
%o A369040 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A369040 A342014(n) = (A003415(n)%n);
%o A369040 Aux369040(n) = [A003415(n), A342014(n)];
%o A369040 v369040 = rgs_transform(vector(up_to, n, Aux369040(n)));
%o A369040 A369040(n) = v369040[n];
%Y A369040 Cf. A003415, A341625, A342014.
%Y A369040 Cf. also A369040, A369050, A369051.
%K A369040 nonn
%O A369040 1,2
%A A369040 _Antti Karttunen_, Jan 18 2024